This paper appertains the presentation of a Clenshaw–Curtis rule to evaluate highly oscillatory Fredholm integro-differential equations (FIDEs) with Cauchy and weak singularities. To calculate singular integral, unknown function approximated by an interpolation polynomial is rewritten as Taylor series expansion. A system linear FIDEs obtained using equally spaced points collocation solved obtai...

This study introduced new technique which is based on a combination of the least-squares (LST) with Chebyshev and Legendre polynomials for finding approximate solutions higher-order linear Fredholm-Volterra integro-differential equations (FVIDEs) subject to mixed conditions. Two examples second third-order FVIDEs are considered illustrate proposed method, numerical results comprised demonstrate...

In this paper, a useful matrix approach for high-order linear Fredholm integro-differential equations with initial boundary conditions expressed as Lucas polynomials is proposed. Using equationwhich equivalent to set of algebraic the method transforms equation. When compared other methods that have been proposed in literature, numerical results from suggested technique reveal it effective and p...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...

In this paper, we propose a different way for solving systems of nonlinear Fredholm integral equations the second kind. We construct our new strategy in two steps, through beginning with linearization phase system by applying Newton method, then pass to discretization some involved operator using Nystr\"{o}m method. The convergence analysis method is proved under necessary conditions. At last, ...

Abstract In this study, linear Fredholm fractional integro-differential equations (FIDEs) are numerically solved, where the derivative is considered in Caputo sense. work, least squares method (LSM) using a compact combination of shifted Chebyshev polynomials (SCP) first Kind applied to solving class FIDEs. Our aim write unknown function as series SCP, and then reduce problem system algebraic e...